Recall that the standard condition number, [1]}, [2]},
introduced in [3]}, [4]} and still of interest, e.g., [5]}, measuring the correlation between relative error and relative
residual, the distance to the nearest singular matrix and the difficulty,
cost and worse-case accuracy in solving a linear system with \(A\) , is \(\kappa :=|A||A^{-1}|\) . However, estimates of the above with \(\kappa \)  are often
(but not always, [6]}) too rough because they do not consider the size
of solution components in the matrix eigenspaces. Thus, generalizations
exist, such as the Kaporin condition number [7]} and extensions based
on generalized inverses [8]}, that can be used to obtain better
predictions. One important, easy to compute and interpret generalization is
the condition number at the solution, also called the effective condition number.
